Iterative DFS vs Recursive DFS and different elements order

Question

I have written a recursive DFS algorithm to traverse a graph:

void Graph<E, N>::DFS(Node n)
{
    std::cout << ReadNode(n) << " ";

    MarkVisited(n);

    NodeList adjnodes = Adjacent(n);

    NodeList::position pos = adjnodes.FirstPosition();

    while(!adjnodes.End(pos))
    {
        Node adj = adjnodes.ReadList(pos);

        if(!IsMarked(adj))
            DFS(adj);

        pos = adjnodes.NextPosition(pos);
    }
}

Then I have written an iterative DFS algorithm using a stack:

template <typename E, typename N>
void Graph<E, N>::IterativeDFS(Node n)
{
    Stack<Node> stack;

    stack.Push(n);

    while(!stack.IsEmpty())
    {
        Node u = stack.Read();

        stack.Pop();

        if(!IsMarked(u))
        {
            std::cout << ReadNode(u) << " ";

            MarkVisited(u);

            NodeList adjnodes = Adjacent(u);

            NodeList::position pos = adjnodes.FirstPosition();

            while(!adjnodes.End(pos))
            {
                stack.Push(adjnodes.ReadList(pos));

                pos = adjnodes.NextPosition(pos);
            }
        }
    }

My problem is that in a graph in which, for example, I enter the three nodes 'a', 'b', 'c' with arcs ('a', 'b') and ('a', 'c') my output is:

'a', 'b', 'c' with the recursive DFS version, and:

'a', 'c', 'b' with the iterative DFS one.

How could I get the same order? Am I doing something wrong?

Thank you!

Answer 1

Both are valid DFS algorithms. A DFS does not specify which node you see first. It is not important because the order between edges is not defined [remember: edges are a set usually]. The difference is due to the way you handle each node's children.

In the iterative approach: You first insert all the elements into the stack - and then handle the head of the stack [which is the last node inserted] - thus the first node you handle is the last child.

In the recursive approach: You handle each node when you see it. Thus the first node you handle is the first child.

To make the iterative DFS yield the same result as the recursive one - you need to add elements to the stack in reverse order [for each node, insert its last child first and its first child last]